Problem: $f(t) = -7t^{2}+2t+1$ $g(t) = 7t^{2}+t+f(t)$ $ g(f(0)) = {?} $
Explanation: First, let's solve for the value of the inner function, $f(0)$ . Then we'll know what to plug into the outer function. $f(0) = -7(0^{2})+(2)(0)+1$ $f(0) = 1$ Now we know that $f(0) = 1$ . Let's solve for $g(f(0))$ , which is $g(1)$ $g(1) = 7(1^{2})+1+f(1)$ To solve for the value of $g$ , we need to solve for the value of $f(1)$ $f(1) = -7(1^{2})+(2)(1)+1$ $f(1) = -4$ That means $g(1) = 7(1^{2})+1-4$ $g(1) = 4$